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Motivated by the notion of boundary for hyperbolic and $CAT(0)$ groups, M. Bestvina in "Local Homology Properties of Boundaries of Groups" introduced the notion of a (weak) $\mathcal Z$-structure and (weak) $\mathcal Z$-boundary for a group $G$ of type $\mathcal F$ (i.e., having a finite $K(G,1)$ complex), with implications concerning the Novikov conjecture for $G$. Since then, some classes of groups have been shown to admit a weak $\mathcal Z$-structure (see "Weak $\mathcal Z$-structures for some classes of groups" by C.R. Guilbault for example), but the question whether or not every group of type $\mathcal F$ admits such a structure remains open. In this paper, we show that every torsion free one-relator group admits a weak $\mathcal Z$-structure, by showing that they are all properly aspherical at infinity; moreover, in the $1$-ended case the corresponding weak $\mathcal Z$-boundary has the shape of either a circle or a Hawaiian earring depending on whether the group is a virtually surface group or not. Finally, we extend this result to a wider class of groups still satisfying a Freiheitssatz property.

In this paper, we consider an equivalence relation within the class of finitely presented discrete groups attending to their asymptotic topology rather than their asymptotic geometry. More precisely, we say that two finitely presented groups $G$ and $H$ are "proper $2$-equivalent" if there exist (equivalently, for all) finite $2$-dimensional CW-complexes $X$ and $Y$, with $\pi_1(X) \cong G$ and $\pi_1(Y) \cong H$, so that their universal covers $\widetilde{X}$ and $\widetilde{Y}$ are proper $2$-equivalent. It follows that this relation is coarser than the quasi-isometry relation. We point out that finitely presented groups which are $1$-ended and semistable at infinity are classified, up to proper $2$-equivalence, by their fundamental pro-group, and we study the behaviour of this relation with respect to some of the main constructions in combinatorial group theory. A (finer) similar equivalence relation may also be considered for groups of type $F_n, n \geq 3$, which captures more of the large-scale topology of the group. Finally, we pay special attention to the class of those groups $G$ which admit a finite $2$-dimensional CW-complex $X$ with $\pi_1(X) \cong G$ and whose universal cover $\widetilde{X}$ has the proper homotopy type of a $3$-manifold. We show that if such a group $G$ is $1$-ended and semistable at infinity then it is proper $2$-equivalent to either ${\mathbb Z} \times {\mathbb Z} \times {\mathbb Z}$, ${\mathbb Z} \times {\mathbb Z}$ or ${\mathbb F}_2 \times {\mathbb Z}$ (here, ${\mathbb F}_2$ is the free group on two generators). As it turns out, this applies in particular to any group $G$ fitting as the middle term of a short exact sequence of infinite finitely presented groups, thus classifying such group extensions up to proper $2$-equivalence.

Statistical analyses from exoplanet surveys around low-mass stars indicate that super-Earth and Neptune-mass planets are more frequent than gas giants around such stars, in agreement with core accretion theory of planet formation. Using precise radial velocities derived from visual and near-infrared spectra, we report the discovery of a giant planet with a minimum mass of 0.46 Jupiter masses in an eccentric 204-day orbit around the very low-mass star GJ 3512. Dynamical models show that the high eccentricity of the orbit is most likely explained from planet-planet interactions. The reported planetary system challenges current formation theories and puts stringent constraints on the accretion and migration rates of planet formation and evolution models, indicating that disc instability may be more efficient in forming planets than previously thought., Comment: Manuscript author version. 41 pages, 11 figures

We present the first part of an investigation on the planetary nebula (PN) PC 22 which focuses on the use of deep imaging and high resolution echelle spectroscopy to perform a detailed morpho-kinematical analysis. PC 22 is revealed to be a multipolar PN emitting predominantly in [O III] and displaying multiple non-symmetric outflows. Its central region is found to be also particularly inhomogeneous with a series of low ionization structures (knots) located on the path of the outflows. The morpho-kinematical model obtained with SHAPE indicates that i) the de-projected velocities of the outflows are rather large, > 100 km/s, while the central region has expansion velocities in the range ~25 to ~45 km/s following the "Wilson effect", ii) the majority of the measured structures share similar inclination, ~100 degrees, i.e. they are coplanar, and iii) all outflows and lobes are coeval (within the uncertainties). All these results make us to suggest that PC 22 is an evolved starfish PN. We propose that the mechanism responsible for the morphology of PC 22 consists of a wind-shell interaction, where the fast post-AGB wind flows through a filamentary AGB shell with some large voids., Comment: Accepted for publication in Monthly Notices of the Royal Astronomical Society Main Journal

In this paper we present the results of optical high-resolution imaging and spectroscopy of the complex planetary nebula (PN) NGC~3242. Our study is based on the analysis of the narrowband H$\alpha$ $\lambda$6563\AA , [O III] $\lambda$5007\AA , [N II] $\lambda$6584\AA , and [S II] $\lambda$6724{\AA} images, and high- resolution spectroscopy using spectral ranges centered on the H$\alpha$ $\lambda$6564\AA , [N II] $\lambda$6583\AA , and [O III] $\lambda$5007\AA . We detected and analysed morphological components beyond the multiple shell structure of this PN, to investigate the small-scale morphological components aligned towards its major axis (such as knots and ansae, as well as the arc-like features) and its surroundings. Thus, we investigated the morpho-kinematical properties of NGC~3242, as well as their nature and formation. Our results regarding the elliptical double-shell structure and the distance to this nebula are in concordance with previous studies. Furthermore, we have used the software SHAPE to construct a 3D model of NGC~3242, allowing us to successfully reproduce our observational data. We conclude that the prominent knots emitting in the [N II] line are fast, low-ionisation emission regions (FLIERs) related to high velocity jets and the so-called ansae-like features rather resemble bubbles. The disruptions immersed in the halo, whose emission was detected in the the [O III] high-excitation emission line, remarkably display high velocities and were formed likely in an earlier ejection event, in comparison to the innermost FLIERs and bubbles. Finally, according to our model, the kinematical ages of the structures in NGC~3242 range from 390 to 5400 yr., Comment: 10 pages, 5 figures, 3 tables. Accepted by MNRAS

We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general topology concerning homogeneous spaces.

CARMENES has been proposed as a next-generation instrument for the 3.5m Calar Alto Telescope. Its objective is finding habitable exoplanets around M dwarfs through radial velocity measurements (m/s level) in the near-infrared. Consequently, the NIR spectrograph is highly constraint regarding thermal/mechanical requirements. As a first approach, the thermal stability has been limited to \pm 0.01K (within year period) over a working temperature of 243K. This can be achieved by means of several temperature-controlled rooms. The options considered to minimise the complexity of the thermal design are here presented, as well as the transient-state thermal analyses realised to make the best choice.

How different is the universal cover of a given finite 2-complex from a 3-manifold (from the proper homotopy viewpoint)? Regarding this question, we recall that a finitely presented group $G$ is said to be properly 3-realizable if there exists a compact 2-polyhedron $K$ with $\pi_1(K) \cong G$ whose universal cover $\tilde{K}$ has the proper homotopy type of a PL 3-manifold (with boundary). In this paper, we study the asymptotic behavior of finitely generated one-relator groups and show that those having finitely many ends are properly 3-realizable, by describing what the fundamental pro-group looks like, showing a property of one-relator groups which is stronger than the QSF property of Brick (from the proper homotopy viewpoint) and giving an alternative proof of the fact that one-relator groups are semistable at infinity.

In this paper, we present the preliminary optical design of PANIC (PAnoramic Near Infrared camera for Calar Alto), a wide-field infrared imager for the Calar Alto 2.2 m telescope. The camera optical design is a folded single optical train that images the sky onto the focal plane with a plate scale of 0.45 arcsec per 18 micron pixel. A mosaic of four Hawaii 2RG of 2k x 2k made by Teledyne is used as detector and will give a field of view of 31.9 arcmin x 31.9 arcmin. This cryogenic instrument has been optimized for the Y, J, H and K bands. Special care has been taken in the selection of the standard IR materials used for the optics in order to maximize the instrument throughput and to include the z band. The main challenges of this design are: to produce a well defined internal pupil which allows reducing the thermal background by a cryogenic pupil stop; the correction of off-axis aberrations due to the large field available; the correction of chromatic aberration because of the wide spectral coverage; and the capability of introduction of narrow band filters (~1%) in the system minimizing the degradation in the filter passband without a collimated stage in the camera. We show the optomechanical error budget and compensation strategy that allows our as built design to met the performances from an optical point of view. Finally, we demonstrate the flexibility of the design showing the performances of PANIC at the CAHA 3.5m telescope., Comment: This paper has been presented in the SPIE of Astronomical Telescopes and Instrumentation 2008 in Marseille (France)

This paper describes how it is possible to increase GP Computing Power via Volunteer Computing (VC) using the BOINC framework. Two experiments using well-known GP tools -Lil-gp & ECJ- are performed in order to demonstrate the benefit of using VC in terms of computing power and speed up. Finally we present an extension of the model where any GP tool or framework can be used inside BOINC regardless of its programming language, complexity or required operating system., Comment: First draft, preparing for PPSN 2008

In this paper, we show that the class of all properly 3-realizable groups is closed under amalgamated free products (and HNN-extensions) over finite groups. We recall that $G$ is said to be properly 3-realizable if there exists a compact 2-polyhedron $K$ with $\pi_1(K) \cong G$ and whose universal cover $\tilde{K}$ has the proper homotopy type of a 3-manifold (with boundary)., Comment: J. Pure Appl. Alg., to appear

We present calculations of the spin-averaged pair distribution function $g(r)$ in a homogeneous gas of electrons moving in dimensionality D=3 or D=2 at finite temperature. The model involves the solution of a two-electron scattering problem via an effective potential which embodies many-body effects through a self-consistent Hartree approximation, leading to two-body wave functions to be averaged over a temperature-dependent distribution of relative momentum for electron pairs. We report illustrative numerical results for $g(r)$ in an intermediate-coupling regime and interpret them in terms of changes of short-range order with increasing temperature., Comment: 6 pages, 5 figures, submitted to Solid State Communications